If it's just filtered out in the training sets, adding the information as context should work out fine - after all this is exactly how o3, Gemini 2.5 and co deal with information that is newer than their training data cutoff.

You can fine tune a model with new information, but it is not the same thing as training it from scratch, and can only get you so far.

You might even be able to poison a model against being fine-tuned on certain information, but that's just a conjecture.

Yes, RAG is one way to do that.